How do you delete drawers in the new wardrobe?

I don't think there is a way to do that right now. :(

A lot of people have been bringing it up since the new wardrobe was released, but I have no idea if it's being worked on or anything.

you are not an idiot. You can't do it at all and it's never been possible with this Wardrobe version. My own wild guess is that if they do fix this it will not happen until Vesnali is over.